You either have some out of date Web Browser plugins (Flash is a reliable crasher of browsers on a Mac) or your RAM is bad or the hard disk has some issues.
Software wise:
There are folders for browser plugins located at:
/Library/Internet Plug-ins/
And (your home folder):
~/Library/Internet Plug-ins/
Take all the plugins out, put them on the desktop and close/reopen the browser. If it stops crashing, its a plugin. Move one back at a time, QuickTime then Flash, maybe Flip4Mac (Windows Media player). If it starts crashing it was the last plugin.
Could also be corrupted System files. Archive and install from the System disc, if you have the time.
Hardware wise:
If you get crashes without any plugin, you might have either a bad stick of RAM or some problem on the Hard Drive. Take it to an Apple store or tech guy and have them swap RAM sticks out and/or run a disk utility on the Hard Drive.
If none of that helps, it may just be the websites you visit. There are many web browsers on the market such as Firefox 3.5 (new today) and Safari-based ones like Google Chrome.
I have had *zero* problems with Safari 4 since the developer previews, except for some changes in rendering that differ significantly from IE7/Firefox.
Part of my job is to make web-based apps (and custom browser plugins for the Mac) so I have to use all manner of browsers and be as compliant as possible, and Safari 4 is the best browser for consistent rendering to the HTML/CSS specs IMO. Google Chrome uses the same underlying HTML engine as Safari 4, so other than looking/working differently as a web browser it renders the same as Safari 4.